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id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Cambiar a la tabla de contenidos" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Cambiar a la tabla de contenidos</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Neper</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Ir a un artículo en otro idioma. Disponible en 35 idiomas" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-35" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">35 idiomas</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D9%8A%D8%A8%D8%B1" title="نيبر – árabe" lang="ar" hreflang="ar" data-title="نيبر" data-language-autonym="العربية" data-language-local-name="árabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9D%D0%B5%D0%BF%D0%B5%D1%80" title="Непер – bielorruso" lang="be" hreflang="be" data-title="Непер" data-language-autonym="Беларуская" data-language-local-name="bielorruso" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Neper" title="Neper – catalán" lang="ca" hreflang="ca" data-title="Neper" data-language-autonym="Català" data-language-local-name="catalán" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Neper" title="Neper – checo" lang="cs" hreflang="cs" data-title="Neper" data-language-autonym="Čeština" data-language-local-name="checo" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Neper" title="Neper – danés" lang="da" hreflang="da" data-title="Neper" data-language-autonym="Dansk" data-language-local-name="danés" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Neper_(Hilfsma%C3%9Feinheit)" title="Neper (Hilfsmaßeinheit) – alemán" lang="de" hreflang="de" data-title="Neper (Hilfsmaßeinheit)" data-language-autonym="Deutsch" data-language-local-name="alemán" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Neper" title="Neper – inglés" lang="en" hreflang="en" data-title="Neper" data-language-autonym="English" data-language-local-name="inglés" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Nepero" title="Nepero – esperanto" lang="eo" hreflang="eo" data-title="Nepero" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%86%D9%BE%D8%B1" title="نپر – persa" lang="fa" hreflang="fa" data-title="نپر" data-language-autonym="فارسی" data-language-local-name="persa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/N%C3%A9per" title="Néper – francés" lang="fr" hreflang="fr" data-title="Néper" data-language-autonym="Français" data-language-local-name="francés" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Neper" title="Neper – gallego" lang="gl" hreflang="gl" data-title="Neper" data-language-autonym="Galego" data-language-local-name="gallego" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Neper" title="Neper – croata" lang="hr" hreflang="hr" data-title="Neper" data-language-autonym="Hrvatski" data-language-local-name="croata" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Neper" title="Neper – húngaro" lang="hu" hreflang="hu" data-title="Neper" data-language-autonym="Magyar" data-language-local-name="húngaro" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%86%D5%A5%D5%BA%D5%A5%D6%80_(%D5%B9%D5%A1%D6%83%D5%B4%D5%A1%D5%B6_%D5%B4%D5%AB%D5%A1%D5%BE%D5%B8%D6%80)" title="Նեպեր (չափման միավոր) – armenio" lang="hy" hreflang="hy" data-title="Նեպեր (չափման միավոր)" data-language-autonym="Հայերեն" data-language-local-name="armenio" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Neper" title="Neper – italiano" lang="it" hreflang="it" data-title="Neper" data-language-autonym="Italiano" data-language-local-name="italiano" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%8D%E3%83%BC%E3%83%91" title="ネーパ – japonés" lang="ja" hreflang="ja" data-title="ネーパ" data-language-autonym="日本語" data-language-local-name="japonés" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9C%E1%83%94%E1%83%9E%E1%83%94%E1%83%A0%E1%83%98" title="ნეპერი – georgiano" lang="ka" hreflang="ka" data-title="ნეპერი" data-language-autonym="ქართული" data-language-local-name="georgiano" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9D%D0%B5%D0%BF%D0%B5%D1%80" title="Непер – kazajo" lang="kk" hreflang="kk" data-title="Непер" data-language-autonym="Қазақша" data-language-local-name="kazajo" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%84%A4%ED%8D%BC" title="네퍼 – coreano" lang="ko" hreflang="ko" data-title="네퍼" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Neperis" title="Neperis – lituano" lang="lt" hreflang="lt" data-title="Neperis" data-language-autonym="Lietuvių" data-language-local-name="lituano" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9D%D0%B5%D0%BF%D0%B5%D1%80" title="Непер – macedonio" lang="mk" hreflang="mk" data-title="Непер" data-language-autonym="Македонски" data-language-local-name="macedonio" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Neper" title="Neper – neerlandés" lang="nl" hreflang="nl" data-title="Neper" data-language-autonym="Nederlands" data-language-local-name="neerlandés" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Neper" title="Neper – noruego nynorsk" lang="nn" hreflang="nn" data-title="Neper" data-language-autonym="Norsk nynorsk" data-language-local-name="noruego nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Neper" title="Neper – polaco" lang="pl" hreflang="pl" data-title="Neper" data-language-autonym="Polski" data-language-local-name="polaco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Neper" title="Neper – portugués" lang="pt" hreflang="pt" data-title="Neper" data-language-autonym="Português" data-language-local-name="portugués" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9D%D0%B5%D0%BF%D0%B5%D1%80" title="Непер – ruso" lang="ru" hreflang="ru" data-title="Непер" data-language-autonym="Русский" data-language-local-name="ruso" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Neper" title="Neper – siciliano" lang="scn" hreflang="scn" data-title="Neper" data-language-autonym="Sicilianu" data-language-local-name="siciliano" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Neper" title="Neper – esloveno" lang="sl" hreflang="sl" data-title="Neper" data-language-autonym="Slovenščina" data-language-local-name="esloveno" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Neper" title="Neper – sueco" lang="sv" hreflang="sv" data-title="Neper" data-language-autonym="Svenska" data-language-local-name="sueco" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9D%D0%B5%D0%BF%D0%B5%D1%80" title="Непер – tayiko" lang="tg" hreflang="tg" data-title="Непер" data-language-autonym="Тоҷикӣ" data-language-local-name="tayiko" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%99%E0%B9%80%E0%B8%9B%E0%B8%AD%E0%B8%A3%E0%B9%8C" title="เนเปอร์ – tailandés" lang="th" hreflang="th" data-title="เนเปอร์" data-language-autonym="ไทย" data-language-local-name="tailandés" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Neper" title="Neper – turco" lang="tr" hreflang="tr" data-title="Neper" data-language-autonym="Türkçe" data-language-local-name="turco" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9D%D0%B5%D0%BF%D0%B5%D1%80_(%D0%BE%D0%B4%D0%B8%D0%BD%D0%B8%D1%86%D1%8F_%D0%B2%D0%B8%D0%BC%D1%96%D1%80%D1%8E%D0%B2%D0%B0%D0%BD%D0%BD%D1%8F)" title="Непер (одиниця вимірювання) – ucraniano" lang="uk" hreflang="uk" data-title="Непер (одиниця вимірювання)" data-language-autonym="Українська" data-language-local-name="ucraniano" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Neper" title="Neper – uzbeko" lang="uz" hreflang="uz" data-title="Neper" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbeko" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%A5%88%E5%9F%B9" title="奈培 – chino" lang="zh" hreflang="zh" data-title="奈培" data-language-autonym="中文" data-language-local-name="chino" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q50094#sitelinks-wikipedia" title="Editar enlaces interlingüísticos" class="wbc-editpage">Editar enlaces</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Espacios de nombres"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Neper" title="Ver la página de contenido [c]" accesskey="c"><span>Artículo</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Discusi%C3%B3n:Neper" rel="discussion" title="Discusión acerca de la página [t]" accesskey="t"><span>Discusión</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Cambiar variante de idioma" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">español</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Vistas"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Neper"><span>Leer</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Neper&action=edit" title="Editar esta página [e]" accesskey="e"><span>Editar</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Neper&action=history" title="Versiones anteriores de esta página [h]" accesskey="h"><span>Ver historial</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Página de herramientas"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Herramientas" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Herramientas</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Herramientas</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">mover a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">ocultar</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Más opciones" > <div class="vector-menu-heading"> Acciones </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Neper"><span>Leer</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Neper&action=edit" title="Editar esta página [e]" accesskey="e"><span>Editar</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Neper&action=history"><span>Ver historial</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Especial:LoQueEnlazaAqu%C3%AD/Neper" title="Lista de todas las páginas de la wiki que enlazan aquí [j]" accesskey="j"><span>Lo que enlaza aquí</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Especial:CambiosEnEnlazadas/Neper" rel="nofollow" title="Cambios recientes en las páginas que enlazan con esta [k]" accesskey="k"><span>Cambios en enlazadas</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=es" title="Subir archivos [u]" accesskey="u"><span>Subir archivo</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Especial:P%C3%A1ginasEspeciales" title="Lista de todas las páginas especiales [q]" accesskey="q"><span>Páginas especiales</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Neper&oldid=158180067" title="Enlace permanente a esta versión de la página"><span>Enlace permanente</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Neper&action=info" title="Más información sobre esta página"><span>Información de la página</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Especial:Citar&page=Neper&id=158180067&wpFormIdentifier=titleform" title="Información sobre cómo citar esta página"><span>Citar esta página</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Especial:Acortador_de_URL&url=https%3A%2F%2Fes.wikipedia.org%2Fwiki%2FNeper"><span>Obtener URL acortado</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a 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<div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Apariencia</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mover a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ocultar</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">De Wikipedia, la enciclopedia libre</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="es" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Archivo:John_Napier.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/John_Napier.jpg/220px-John_Napier.jpg" decoding="async" width="220" height="278" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/e/e3/John_Napier.jpg 1.5x" data-file-width="317" data-file-height="400" /></a><figcaption>Retrato de John Napier (1550-1617), inventor de los logaritmos.</figcaption></figure> <dl><dd><i>Este artículo es sobre una unidad de medida. Sobre el matemático escocés, véase <a href="/wiki/John_Napier" title="John Napier">John Napier</a></i></dd></dl> <p>El <b>neper</b> o <b>neperio</b> (<b>Np</b>) es una <a href="/wiki/Unidad_de_medida" title="Unidad de medida">unidad de medida</a> relativa que se utiliza frecuentemente en el campo de la <a href="/wiki/Telecomunicaci%C3%B3n" title="Telecomunicación">telecomunicación</a>, para expresar relaciones entre <a href="/wiki/Voltaje" class="mw-redirect" title="Voltaje">voltajes</a> o <a href="/wiki/Intensidad_de_corriente_el%C3%A9ctrica" class="mw-redirect" title="Intensidad de corriente eléctrica">intensidades</a>. Su nombre procede de <a href="/wiki/John_Napier" title="John Napier">John Napier</a>, el inventor de los <a href="/wiki/Logaritmo" title="Logaritmo">logaritmos</a>.<br /> Aunque no es una unidad de medida del <a href="/wiki/Sistema_Internacional_de_Unidades" title="Sistema Internacional de Unidades">Sistema Internacional</a>, su uso es ampliamente aceptado en muchos países, para los mismos fines que el <a href="/wiki/Decibelio" title="Decibelio">decibelio</a>. La diferencia fundamental entre ambas unidades es que mientras el decibelio está basado en el logaritmo decimal de la relación de magnitudes, el neperio lo está en el <a href="/wiki/Logaritmo#Logaritmo_neperiano" title="Logaritmo">logaritmo natural</a> o neperiano de la citada relación, viniendo el número de nepers determinado por la fórmula: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Np=\ln {\frac {x_{1}}{x_{2}}}=\ln x_{1}-\ln x_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mi>p</mi> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <mi>ln</mi> <mo>⁡</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Np=\ln {\frac {x_{1}}{x_{2}}}=\ln x_{1}-\ln x_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/91af60f126ceca0e05f92bf0e343da605cfba733" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:27.238ex; height:5.009ex;" alt="{\displaystyle Np=\ln {\frac {x_{1}}{x_{2}}}=\ln x_{1}-\ln x_{2}}"></span></dd></dl> <p>donde <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{1}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{1}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e43e4dbe894c6812fc4ef377bafc4dc5ff14ce4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.771ex; height:2.009ex;" alt="{\displaystyle x_{1}\,}"></span> y <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e3892c72a14aa6e51f1d169e5082e2a1cd961765" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.771ex; height:2.009ex;" alt="{\displaystyle x_{2}\,}"></span> son los valores relacionados, y <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ln \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ln</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ln \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72bace799d1397bad584350c3f9e8fa24a3c7509" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.326ex; height:2.176ex;" alt="{\displaystyle \ln \,}"></span> el logaritmo natural. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Relación_con_el_decibelio"><span id="Relaci.C3.B3n_con_el_decibelio"></span>Relación con el decibelio</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Neper&action=edit&section=1" title="Editar sección: Relación con el decibelio"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>El neper se utiliza mayormente para expresar relaciones entre <a href="/wiki/Voltaje" class="mw-redirect" title="Voltaje">voltajes</a> o <a href="/wiki/Intensidad_de_corriente_el%C3%A9ctrica" class="mw-redirect" title="Intensidad de corriente eléctrica">intensidades</a> mientras que el decibelio, es más utilizado para expresar relaciones entre <a href="/wiki/Potencia_el%C3%A9ctrica" title="Potencia eléctrica">potencias</a>. Teniendo esto en cuenta se puede establecer la relación entre ambas unidades a partir de una relación de voltajes: </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{1 Np}}=\ln {\frac {V_{1}}{V_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>1 Np</mtext> </mrow> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{1 Np}}=\ln {\frac {V_{1}}{V_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0fbc4f048039aca2a10404c94ee5d4219877625c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.449ex; height:5.509ex;" alt="{\displaystyle {\text{1 Np}}=\ln {\frac {V_{1}}{V_{2}}}}"></span></center> <p>por lo que: </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {V_{1}}{V_{2}}}=e=2,71828182846}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mi>e</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>71828182846</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {V_{1}}{V_{2}}}=e=2,71828182846}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f8fe72c721d5059c4abae45c116e9e801ce3229" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:25.509ex; height:5.509ex;" alt="{\displaystyle {\frac {V_{1}}{V_{2}}}=e=2,71828182846}"></span></center> <p>La correspondencia de Np a dB de la misma magnitud física, <a href="/wiki/Id_est" title="Id est">i.e.</a>, potencia con potencia o intensidad con intensidad es: </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1{\text{Np}}=10\log(e)dB\approx 4,343{\text{dB}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext>Np</mtext> </mrow> <mo>=</mo> <mn>10</mn> <mi>log</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>e</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>B</mi> <mo>≈</mo> <mn>4</mn> <mo>,</mo> <mn>343</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1{\text{Np}}=10\log(e)dB\approx 4,343{\text{dB}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96b3448afdb4b32076d668b76c1464d4877838be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.573ex; height:2.843ex;" alt="{\displaystyle 1{\text{Np}}=10\log(e)dB\approx 4,343{\text{dB}}}"></span></center> <p>La equivalencia anterior está prohibida en telecomunicaciones para evitar ambigüedades.<sup id="cite_ref-1" class="reference separada"><a href="#cite_note-1"><span class="corchete-llamada">[</span>1<span class="corchete-llamada">]</span></a></sup> En este campo se debe utilizar obligatoriamente la obtenida si se calcula cuántos decibelios corresponden a esta relación de tensiones, con la relación de potencias se tiene: </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1{\text{Np(intensidad)}}=20\log(e)dB(potencia)\approx 8,686{\text{dB (potencia)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext>Np(intensidad)</mtext> </mrow> <mo>=</mo> <mn>20</mn> <mi>log</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>e</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>B</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mi>o</mi> <mi>t</mi> <mi>e</mi> <mi>n</mi> <mi>c</mi> <mi>i</mi> <mi>a</mi> <mo stretchy="false">)</mo> <mo>≈</mo> <mn>8</mn> <mo>,</mo> <mn>686</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB (potencia)</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1{\text{Np(intensidad)}}=20\log(e)dB(potencia)\approx 8,686{\text{dB (potencia)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25af03716049cf2b254bd38f511062d95c066eb4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:64.242ex; height:2.843ex;" alt="{\displaystyle 1{\text{Np(intensidad)}}=20\log(e)dB(potencia)\approx 8,686{\text{dB (potencia)}}}"></span></center> <p>Aunque, como se ha dicho, se puede utilizar para relaciones de potencias, voltajes o intensidades, en el caso de potencias y teniendo en cuenta que: </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P={\frac {V^{2}}{R}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>R</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P={\frac {V^{2}}{R}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e58706dc818e0d1389df4be6028c0566639ab70f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.651ex; height:5.843ex;" alt="{\displaystyle P={\frac {V^{2}}{R}}}"></span></center> <p>el valor en nepers queda determinado por la fórmula: </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{Np}}=0,5\cdot \ln {\frac {P_{1}}{P_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Np</mtext> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>5</mn> <mo>⋅</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{Np}}=0,5\cdot \ln {\frac {P_{1}}{P_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c790ee5a1238d6022d751e0cae3f9890ca025a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:16.881ex; height:5.509ex;" alt="{\displaystyle {\text{Np}}=0,5\cdot \ln {\frac {P_{1}}{P_{2}}}}"></span></center> <p>Al igual que el <a href="/wiki/Decibelio" title="Decibelio">decibelio</a>, el neper es una unidad adimensional, estando el uso de ambas unidades reconocido por la <a href="/wiki/Uni%C3%B3n_Internacional_de_Telecomunicaciones" title="Unión Internacional de Telecomunicaciones">Unión Internacional de Telecomunicaciones</a> (UIT) y por el Sistema Internacional de Pesos y Medidas (S.I.). </p> <div class="mw-heading mw-heading2"><h2 id="Véase_también"><span id="V.C3.A9ase_tambi.C3.A9n"></span>Véase también</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Neper&action=edit&section=2" title="Editar sección: Véase también"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Decibelio" title="Decibelio">Decibelio</a></li> <li><a href="/wiki/Fonio" title="Fonio">Fonio</a></li> <li><a href="/wiki/Sonio" title="Sonio">Sonio</a></li> <li><a href="/wiki/Ac%C3%BAstica" title="Acústica">Acústica</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Referencias">Referencias</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Neper&action=edit&section=3" title="Editar sección: Referencias"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="listaref" style="list-style-type: decimal;"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><span class="citation web"><a rel="nofollow" class="external text" href="https://www.itu.int/dms_pubrec/itu-r/rec/v/R-REC-V.574-5-201508-I!!PDF-E.pdf">«Use of the decibel and the neper in telecommunications - ITU (International Telecommunications Union)»</a>.</span><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fes.wikipedia.org%3ANeper&rft.btitle=Use+of+the+decibel+and+the+neper+in+telecommunications+-+ITU+%28International+Telecommunications+Union%29&rft.genre=book&rft_id=https%3A%2F%2Fwww.itu.int%2Fdms_pubrec%2Fitu-r%2Frec%2Fv%2FR-REC-V.574-5-201508-I%21%21PDF-E.pdf&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Enlaces_externos">Enlaces externos</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Neper&action=edit&section=4" title="Editar sección: Enlaces externos"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20100105214905/http://agamenon.tsc.uah.es/Asignaturas/ie/sis_com/apuntes/Unidades_Logaritmicas.pdf">El Decibelio y el Neperio</a></li></ul> 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